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The Elliptic Curve Method : A Modern Approach to Integer Factorization

In this paper, we present a study of elliptic curves, focusing on theirunderlying mathematical concepts, properties and applications in numbertheory. We begin by introducing elliptic curves and their unique features,discussing their algebraic structure, and exploring their group law, pro-viding examples and geometric interpretations. The core of our studyfocuses on the Elliptic Curve Method (ECM) for integer factorization.We present the motivation behind ECM and compare it to Pollard’s (p-1) method. A discussion on pseudocurves and the choice of an ellipticcurve and bound B is provided. We also address the differences betweenECM and Pollard’s (p-1) method and propose optimization techniques forECM, including the calculation of the least common multiple (LCM) ofthe first B integers using the Sieve of Eratosthenes.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kth-330276
Date January 2023
CreatorsCao, Felix
PublisherKTH, Skolan för teknikvetenskap (SCI)
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, info:eu-repo/semantics/bachelorThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess
RelationTRITA-SCI-GRU ; 2023:110

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